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Replicant compression coding in Besov spaces

Gérard Kerkyacharian;  Dominique Picard — 2003

ESAIM: Probability and Statistics

We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space B π , q s on a regular domain of ℝ d . The result is: if s - d ( 1 / π - 1 / p ) + > 0 , then the Kolmogorov metric entropy satisfies H ( ϵ ) ∼ ϵ - d / s . This proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound, we provide a new universal...

Replicant compression coding in Besov spaces

Gérard Kerkyacharian;  Dominique Picard — 2010

ESAIM: Probability and Statistics

We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space B π , q s on a regular domain of ℝ d . The result is: if then the Kolmogorov metric entropy satisfies . This proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound, we provide...

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